Talk:Square pyramid#Great Pyramid

I think that the volume of this section is not correct. Please check Wolfram Research, Inc

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http://mathworld.wolfram.com/SquarePyramid.html

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for correct information.

--Kibria100 13:05, 20 June 2006 (UTC)

: The formulae are different because they use different parametrizations. The one given on this page assumes a pyramid with regular faces, edge length a.

:The Johnson pyramid should be "half" a regular octahedron in volume. Looks like an extra sqrt(2) ... I'll remove one!

: Tom Ruen 23:41, 20 June 2006 (UTC)

I removed this:

: Other square pyramids have isosceles triangle sides. For example the Great Pyramid of Giza has isosceles triangles of base 756 feet and slant height 719 feet. That pyramid has the interesting property that the slant height (along the bisector of a face) is very nearly equal to the golden ratio times the height, in which case the area of each triangular face is equal to the square of the pyramid's height.

If the base is 756 ft and the slant-height is 719 ft, then the height is 612 ft; 719:612 is nowhere near the golden ratio. —Tamfang (talk) 21:24, 6 April 2009 (UTC)

:You're right, it was wrong. You can find the correct relationship and some sources at golden ratio#Pyramids. Dicklyon (talk) 04:13, 7 April 2009 (UTC)

It may be worth mentioning in the "Other square pyramids" section, the pyramid (with apex above base centre) which has a height exactly half of the base length; this is the type of pyramid yielded by slicing a cube into six identical pyramids, and hence it is capable of entirely filling a 3D space without leaving any gaps, and without the help of any other polyhedron.

Also, by sticking six such pyramids to the faces of a cube, the result is a rhombic dodecahedron, and this could be mentioned in the "Related polyhedra and honeycombs" section. Certainly that section should be clarified a bit, regarding the tetrakis hexahedron; it should be mentioned that by "short" is meant a pyramid the height of which is less than half of the length of the base.

If citations can be found, these would be worthy additions. — 2A02:C7D:419:2500:207F:B0B3:C1A7:E60B (talk) 09:17, 3 June 2017 (UTC)

:I support all these suggestions (above). --JavBol (talk) 20:00, 10 October 2021 (UTC)

@Administrator {{U|David Eppstein}}: Sorry for bothering you with an infobox again... But the infobox of the Square pyramid article should treat only the equilateral square pyramid, shouldn't it? In advance, thank you for your answer! --JavBol (talk) 20:35, 10 October 2021 (UTC)

:Why? If this article is about all kinds of square pyramids, what is the justification for ignoring that and only considering a special case in the infobox, as if it were an article with a different focus? —David Eppstein (talk) 04:16, 11 October 2021 (UTC)

::Because for the Antiprism article, you told me (on your talk page, i think) to make its infobox focus on convex uniform antiprisms, & you insisted on uniformity more than convexity. Of course, the equilateral square pyramid is not uniform; but it has regular faces. Besides: the head section's 3 figures have regular faces; & the infobox's "Type" row specifies "Johnson J₁". --JavBol (talk) 14:57, 11 October 2021 (UTC)

::@{{U|David Eppstein}}: But all right square pyramids have the same symmetry group & rotation group, so perhaps this infobox should focus on right square pyramids? Then, "Johnson J₁" should be removed from this infobox's "Type" row, shouldn't it? --JavBol (talk) 15:55, 12 October 2021 (UTC)

{{Talk:Square pyramid/GA1}}

@Dedhert.Jr: In response to your edit summary, I'd support a full switch to {{tl|sfn}} citations. I was going to go through and do some cleanup with the references anyways, so I might just do both at the same time if you're alright with that. —TechnoSquirrel69 (sigh) 19:47, 20 November 2023 (UTC)

:@TechnoSquirrel69 Short citations may be also used for notes, so I agree about to convert them. I will do the cleanup right now. Dedhert.Jr (talk) 23:25, 20 November 2023 (UTC)

::Done! I have made some changes here, converting to sfnp and pull down the references. Let me know what do you think. Dedhert.Jr (talk) 00:36, 21 November 2023 (UTC)

{{Template:Did you know nominations/Square pyramid}}

@David Eppstein. I'm considering expanding the properties section that includes the height, surface area, and volume of an equilateral square pyramid. Its height can be expressed as $\backslash sqrt\{1/2\}\; \backslash approx\; 0.707$, but the source I have found [https://books.google.com/books?id=Ws6-DwAAQBAJ&pg=PA123 source I have found] explains the case of the unit edge. Does it count as WP:CALC if I multiply that height with random edge length $a$? An alternative source is from [https://www.problemasyecuaciones.com/geometria3D/volumen/Johnson/J1/calculadora-area-volumen-formulas.html Spanish language], but I'm skeptical whether reliable or not. Dedhert.Jr (talk) 11:51, 31 January 2024 (UTC)

:I'd rather go with a good book source and count the scalar factor as the sort of simple calculation allowed by WP:CALC. —David Eppstein (talk) 17:05, 31 January 2024 (UTC)